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GARP.2012.PQ.P1 American Options, Effects of Dividends, Early Exercise (garp12-p1-19)


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Thread starter #1
Question: Sam Seel has a small portfolio of options. Since the options are currently in-the-money, he is considering the possibility of early exercise. Which of the following statements is correct?

a. It is never optimal to exercise European call options early.
b. It is best to exercise a put option when it is just in-the-money.
c. Early exercise of put options becomes more attractive when interest rates rise.
d. Early exercise of put options becomes more attractive when interest rates decline.

Answer: c

Explanation:When interest rates rise, stock prices have a tendency to fall. This increases the value of a put option on a stock. All options benefit from high volatility.

Could someone please help to advise on this? I thought an increase in interest rates would cause the put option value to decrease and not increase?


Aleksander Hansen

Well-Known Member
a) looks tempting but is incorrect since one cannot exercise early. Would perhaps argue this is misleading since it is never optimal to exercise early because it is not possible. Answer option should be rephrased or changed.

C) While true, the reason given violates the ceteris paribus assumption and is thus a poor explanation (although it can be true it doesn't have to be if you let all variables float around). Again, it should be qualified by American put option.

You would usually be correct in that it reduces the value of the put. However, you have to read between the lines here: it's talking about potential early exercise when rates are increasing....is that ever optimal?
As r increases sufficiently it can be shown that the interest you expect to earn on your strike is weakly stochastically dominating the value of the optionality and insurance a put option offers.
Hi ert,

I was confused for the same reasons at first.

The catch here is that we are going to Exercising the option. It no longer matters how the price of the option changes if we decide to exercise. Hence the 6 factors that changes option prices should be out of the picture.

We should now only consider factors that impact the value of the proceeds from the exercise.

Makes sense?

David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi @HTHNIK I moved to prexisting thread where you can see Aleks (who knows his stuff) answered this smartly. This question is difficult and I agree with him that a better question would add some helpful qualifiers. I copied Hull below (emphasis mine). And I would like to connect this to another, related (and also counter-intuitive) concept: we are told that theta is generally negative, but with two exceptions: 1. a currency call where the interest rate is high, and 2. [related to this question] a deeply in the money European put; i.e., when a put option is deeply in the money, it may be preferable to exercise immediately because the "bird in the hand" (i.e., the intrinsic value realized as cash) outweighs the risk of a future drop in intrinsic value (a risk that increases with a higher interest rate).

Here is Hull:
"Like a call option, a put option can be viewed as providing insurance. A put option, when held in conjunction with the stock, insures the holder against the stock price falling below a certain level. However, a put option is different from a call option in that it may be optimal for an investor to forgo this insurance and exercise early in order to realize the strike price immediately. In general, the early exercise of a put option becomes more attractive as S0 decreases, as r increases, and as the volatility decreases." -- Hull, John C. Options, Futures, and Other Derivatives (9th Edition) (Page 247). Prentice Hall. Kindle Edition.
In the Hull explanation does it mean that as vols decrease, and if an option is ITM we should exercise it because the stock is stable and less likely to move about?


@David Harper CFA FRM regarding the question below, can you please explain to me why D is not the right answer? As risk free rate increases, the value of the put decreases, which makes it less likely to be exercised early. And vise versa, when risk free declines, the value of put options increases which makes it more attractive for early exercise. Thanks!


David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi @thanhtam92 I moved to the previous discussion; I believe this is a flawed question (or at a minimum, it is insufficiently precise) but many of GARP's practice questions are flawed (we don't recommend too much study of their PQs before 2018 where error rate exceeds 30%). Thanks,